CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

mehrozkhn

sol:
let P = ak/(2-a)
we have to find [P]
let a = 1+(x/y) where x,y are integers
x<y , x is not equal to y and none is equal to zero
then P = k + 2kx/(y-x) .....(1)
now the second part in above eqn. Will assume integral values if
x/(y-x) = n where n is integer greater than or equal to 1
=> x = ny/(n+1)
since x,y are integers this will only be possible if y is a multiple of (n+1)
hence in this case
P = k(2n + 1) which is an integer
hence [P] = k(2n + 1) ....(2)
now consider the case where
x/(y-x) = n - e/f
where e<f and both are integers not equal to 0.
Then in this case
P = k(2n+1) - 2ke/f ....(3)
now the second part will be integer if
f is even and equal to
f = 2k/r where r is any integer
in this case P= k(2n+1) - re which is integer
hence [P] = k(2n+1) - re .....(4)
now if 2k is not a multiple of f i.e f is not even
then f is odd i.e. f = 2s +1 where s is any integer
then in this case
P = k(2n+1) - 2ke/(2s + 1) .....(5)
now either 2k>(2s+1) or 2k<(2s+1)
and hence in every case [P] can be found without usin either [X] or [Y]
hence answer is (5) question can be answered using neither [X] nor [Y]

dewan_iitr

Quote:

Originally Posted by swati1606

take condition X

[a[k/(2-a)]+a/2]=p
put [k/(2-a)]=B
thus
[aB+a/2]=p
=> p<=aB+a/2<p+1
=> (p-a/2)<aB<p

now a lies between 1 & 2, thus a/2 lies between 0&1
hence aB=a[k/(2-a)]=p-1

Please explain part in bold
how aB = p-1
min. value is p-1 but max still remains p

swati1606

B is a greatest integer function in itself. so it will take the value of the min integer, which is p-1.

@aarav sir please point out the error in my method

swati1606

oh and 1<a<2
not, 1<=a<=2

sinduja · 05:30 PM

Reduction in speed of an engine is directly proportional to square of the number of bogies attached. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when 5 bogies are attached to it.

can anyone help me in solving this in shorter way?

shivam_01

Quote:

Originally Posted by sinduja

Reduction in speed of an engine is directly proportional to square of the number of bogies attached. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when 5 bogies are attached to it.

can anyone help me in solving this in shorter way?

This is not the appropriate thread to post your quant queries
check this one
http://www.pagalguy.com/forum/quanti...cat08-490.html (official quant thread for cat08)

Aarav

Kindly carry the discussions for QQAD 51 to 100 here
http://www.pagalguy.com/forum/quanti...tions-day.html (CAT 2008: Quantitative Questions a Day 51-100 -The discussions-Brought to you by SMOT)

Aarav

Quote:

Originally Posted by swati1606

B is a greatest integer function in itself. so it will take the value of the min integer, which is p-1.
@aarav sir please point out the error in my method

Please do that yourself. I will write how (X) is sufficient.

Put 2-a = m => 0 < m < 1, we will show that [(2-m)k/m] = [(2-m)[k/m] + (2-m)/2]

[(2-m)k/m] = [2k/m] - k, since k is an integer.

Let us take this case by case.

Case 1: when k/m is an integer = i
[(2-m)k/m] = 2i - k, and [(2-m)[k/m] + (2-m)/2] = [2i -mi + 1-m/2] = [2i -k + 1-m/2] = 2i - k.

Case 2: when i-1/2 < k/m < i, where i is an integer
[(2-m)k/m] = 2i - 1 - k, [(2-m)[k/m] + (2-m)/2] = [2i - m/2 - k] = 2i - 1 - k

Case 3: when i < k/m < i + 1/2, where i is an integer
Prove yourself here that [(2-m)k/m] = [(2-m)[k/m] + (2-m)/2]

=> X is sufficient for all k

vikramchari

Quantitative Question # 052
------------------------------------------------------
Nbangalorekar bought a 10 kg of water-melon in Bangalore that had 99% water. After the water-melon was left outdoors for a day, it was 95% water. What was the weight of the dehydrated water-melon?

(1) 9.6 kg (2) 9.5 kg (3) 2 kg (4) can not be determined (5) none of these

A 10kg watermelon has 9.9kg of water which means that the weight of empty watermelon is 0.1 kg-this remains constant even for the dehydrated watermelon.
Let the wt of dehydrated watermelon be x.
weight of water = 0.95 * x
weight of empty watermelon = x-0.95x = 0.05x
0.05x = 0.1
=> x=2
Answer (3)?

srikar2097

Quote:

Originally Posted by vikramchari

Quantitative Question # 052
------------------------------------------------------
[b][font=Georgia]Nbangalorekar bought a 10 kg of water-melon in Bangalore that had 99% water. After t
=> x=2
Answer (3)?

Not here vikram, post your reply in QQAD 50-100 thread. here (CAT 2008: Quantitative Questions a Day 51-100 -The discussions-Brought to you by SMOT)